98
3 Forced Vibration of Single Degree of Freedom System
Fig. 3.26 Time variation of (DLF) max for a rectangular pulse
3.14 Response Due to Periodic Forces
Forces acting on different systems are often periodic. Any periodic force can be
resolved into a series of harmonic components. We start by introducing real Fourier
series and studying the response of the system to periodic forces (Fig. 3.27).
3.14.1 Real Fourier Series
Consider a periodic function F(t) of period T. This function can be separated into
harmonic components by means of a Fourier series expansion.
The periodic function F(t) is given by
F (t) = a 0 +
∞
n=1
a n cos nω t +
∞
n=1
b n sin nω t
(3.95)
Fig. 3.27 Periodic force
3 Forced Vibration of Single Degree of Freedom System
Fig. 3.26 Time variation of (DLF) max for a rectangular pulse
3.14 Response Due to Periodic Forces
Forces acting on different systems are often periodic. Any periodic force can be
resolved into a series of harmonic components. We start by introducing real Fourier
series and studying the response of the system to periodic forces (Fig. 3.27).
3.14.1 Real Fourier Series
Consider a periodic function F(t) of period T. This function can be separated into
harmonic components by means of a Fourier series expansion.
The periodic function F(t) is given by
F (t) = a 0 +
∞
n=1
a n cos nω t +
∞
n=1
b n sin nω t
(3.95)
Fig. 3.27 Periodic force